Optimization of Stabilizing Systems in Protection of ...

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Optimization of Stabilizing Systems in Protection ofCultural Heritage: The Case of the HistoricalRetaining Wall in the Wisłoujscie Fortress

Piotr Chudoba 1, Jarosław Przewłócki 1, Piotr Samól 1,* and Lesław Zabuski 2

1 Faculty of Architecture, Gdansk Univeristy of Technology, Narutowicz St. 11/12, 80-230 Gdansk, Poland;[email protected] (P.C.); [email protected] (J.P.)

2 Polish Academy of Sciences, Institute of Hydro-Engineering, Koscierska St. 7, 80-328 Gdansk, Poland;[email protected]

* Correspondence: [email protected]

Received: 5 September 2020; Accepted: 12 October 2020; Published: 16 October 2020�����������������

Abstract: The aim of the paper is to propose new quantitative criteria for selecting the optimalmethod of securing and repairing a historical object, which take into account Structural, Conservationand Architectural aspects (the S–C–A method). Construction works on cultural heritage sites tendto be challenging and require an interdisciplinary approach. Therefore, they are strictly relatedto the philosophy of sustainable development which seeks adequate proportions between factorsindicated on the natural and social environment. Optimization of several systems stabilizing retainingstructure that are a historic object was considered in the paper. Appropriate formulas for scoresmeeting additional conservation and aesthetic requirements were proposed. The method is usedin the stabilization of the brick retaining wall, a part of the Wisłoujscie Fortress located in Gdansk,Poland. In order to compute the displacement of the wall and its stability, numerical analysis wasperformed by the two-dimensional explicit Finite Difference Method (using the FLAC2D software).The algorithm proposed could be beneficial to the protection of cultural heritage since it could also beapplied to other structures, such as roof trusses, masonry walls, pillars, etc.

Keywords: multiple-criteria decision-making; optimization; masonry; retaining wall; heritageprotection; stabilizing systems; decision-support system

1. Introduction

Just a few years ago, cultural heritage was out of scope in documents and publications focused onsustainable development. In the famous Burtlandt report [1], architectural and cultural heritage arementioned only twice—always in the context of threats for the whole human environment. Until thelate 1990s, most scientists avoided introducing cultural heritage in the discussion about sustainability,despite its importance for societies. A significant role in changing this situation was played byUNESCO (United Nations Educational, Scientific and Cultural Organization), which organized severalinternational conferences (e.g., in Stockholm in 1998; in Hangzhou in 2013) about the interactionsbetween sustainability and cultural heritage. They allowed incorporation of heritage as an immanentcomponent of social and cultural aspects in the broader concept of sustainable development [2–4].Therefore, the protection of monuments in its economic and social elements might be treated as anessential issue of contemporary modernization processes.

The main concern of civil engineers is to design a safe and cost-effective structure. It can beachieved through an optimization method, which should be an inherent part of all engineering practices.Optimization can be defined as a decision-making process aiming to achieve the best measurableperformance under given constraints. In limit state design, two basic requirements, ultimate limit state

Sustainability 2020, 12, 8570; doi:10.3390/su12208570 www.mdpi.com/journal/sustainability

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(ULS) and serviceability limit state (SLS), must be checked. Structural optimization is the oldest and bestknown approach. It can take the various forms of sizing, shape, topology optimization, etc. Some issuespertaining to structural optimization used in geotechnical engineering are described, for example,in [5,6]. There are also papers referring to optimal design of slope-stabilizing systems, i.e., the subject ofa paper by Yang et al. [7] proposed the optimal design of anchor cables (a reasonable position and length)for slope reinforcement; Hosseinian and Seifabad [8] carried out optimization considering the distancebetween piles in supporting structure; Hajiazizi and Mazaheri [9] took into account the length of piles;Yazdanpanah et al. [10] presented a method of optimizing reinforced layers in slope stabilization design.Usually, costs are a further factor taken into account in the design; economic optimization is mostcommonly used to estimate them. Several more or less advanced economic optimization methods havebeen developed and applied to geotechnical problems. Economic optimization procedures for the designof spread footing have been proposed in [11,12]. In the latter, which—like the current paper—focuseson a reconstruction of retaining wall, a comparative analysis of various optimization methods hasbeen conducted. Wang [13] and Zhang et al. [14], for example, developed a design approach thatintegrates economic design optimization with reliability-based methodologies. This approach allowsfor taking geotechnical uncertainties into account. There are also many construction planning problemsthat require optimizing construction time, quality or sustainability. A review of recent constructionmulti-objective optimization research is given in [15]. Time–cost optimization of construction projectsscheduling, especially important for lengthy and costly projects, is presented in [16]. Chen et al. [17]developed an effective and efficient optimization algorithm of construction time and applied it to acase study involving the construction of a secant pile wall. Yang et al. [18] proposed the simulationoptimization framework (taking account uncertainties), which allows for maintenance planning fordeteriorating bridges.

Protection of historical buildings, especially those at risk of construction failure, involves severalstakeholders, including structural engineers, heritage conservation officers, council architects andvarious other state or local government officials. At the initial stage of a restoration project,numerous consultations with these authorities take place. Conservation officers’ responsibilityis to ensure that conservation values, such as authenticity of the building, are preserved. On the otherhand, while architects manage the whole design process and stress the importance of its aestheticqualities, civil engineers focus on the safety of the structure to prevent its failure. Due to different,and at times conflicting, aims of those involved, differences of opinion may emerge over the methodsof saving, repairing and strengthening the structure, which makes repair works to damaged historicalbuildings a challenge. Consequently, the choosing of the optimal method of the repairing the historicalobjects needs the approach which provides minimal disturbance to the original structure. The methodsof strengthening historical monuments are usually expensive and difficult to implement. Due to thehistorical value of the object, issues relating to costs often become of secondary importance. In thesecases, economic optimization methods cannot be utilized and selecting the optimal interventionmethods to protect such facilities requires a non-standard approach.

A method of choosing the optimal solution for repairing historic construction is proposed inthis paper. This method has been applied to stabilize a historical retaining wall as a special case ofmasonry structure. The authors narrate the history of the wall, based on historical, archaeological andarchitectural evidence, which allowed them to establish the most probable explanation for constructionfailure. Consequently, they propose and discuss several methods that could be applied to repair it.The authors also consider the consequences of those with respect to conservative values, aesthetics ofthe wall and the safety of its structure. In fact, it is an optimization procedure but under additionalconservation and aesthetic constrains. Because the retaining wall is built of brick and earthwork,its reparation would involve intervention in both the brick and earth parts. This means that anyreinforcement of the wall beyond its current outline would necessitate archaeological excavations inthe areas of reinforcement. This choice requires profound knowledge of the properties of the historical

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wall and its foundations, as well as expertise in the methods of repairing and strengthening retainingstructures, slope stabilization methods and in computational analysis.

Interesting outlines of the construction of dry-stone retaining walls and the history of their design,including stability analysis, are given in [19–22]. Reviews of methods applicable to the study of masonryhistorical constructions are presented in [23–25]. Several reviews of analytical methods employed inmasonry are presented in [26–28] and the applicability of different numerical techniques to the analysisof such structures is discussed, for example, by Lourenço et al. [29]. Various aspects of the history offoundation engineering, with particular focus on its development, techniques applied, materials usedand analysis methods, are described in [20,30,31]. Several examples of historical foundations, as well aspast and contemporary preservation techniques, are also presented in the latter.

Buildings set on embankments pose a particular challenge and their structure should beadequately protected. This is usually done by strengthening their foundations or the underlyingsubsoil. Reinforced soil techniques are effective in strengthening historical buildings. There areseveral methods used to protect slopes, such as retaining structures or soil stabilization techniques.Some recommendations as to how they could be applied to historic retaining walls are given in [32,33].The application of ground anchors is reviewed, for example, in [34–36]. The possible uses of relievingshelves are outlined, among others, in [37,38] and those of CFA (continuous flight augering) pilingin [39]. The functioning of buttresses is reviewed in [40], while the utility of widening the wall base isconsidered, for instance, in [41,42]. The applications of nailing are summarized in [35,43,44].

The aim of this paper is to propose a new quantitative criterion for selecting the optimal methodof securing and repairing a wall, which takes into account proper structural (technical), conservationand aesthetic conditions. The analyses included here provide an innovative, never-before-used systemof assessments (the S–C–A method: Structure–Conservation–Architecture). Notably, this new methodmay be implemented only as a result of an interdisciplinary analysis of the historical object, in whichspecialists from different fields of science must cooperate. This approach can be applied to some othercases and it should bring benefits to protect the authenticity of historical structures. The proposedmethod was applied to the retaining wall in one of the most remarkable examples of historic militaryengineering in the country and the entire Baltic Sea Region— the Wisłoujscie Fortress in Gdansk,Poland. Several methods of structure stabilization were considered. For each of them, in order tocompute to determine the displacement of the wall and its stability, numerical analysis was carried outby the two-dimensional explicit Finite Difference Method, using the FLAC2D software [45].

2. The Structure–Conservation–Architecture Methodology

The S–C–A (Structure–Conservation–Architecture) methodology has been developed by theauthors in order to determine the optimal technology to repair historic buildings. The idea of comparingfactors from different fields of knowledge (engineering, architecture, conservation) was based on thetheory of sustainable development that was invented for keeping the balance between economic,social (including cultural) and environmental costs of “progress”. It must be mentioned that currentliterature about cultural heritage in the context of sustainability is focused on landscape values, transportor touristic traffic issues [46], underestimating the relations between economic pressure and preservingthe authenticity of the monument. Therefore, the presented new S-C-A method is focused on preparinga list of proposed technologies and evaluating the influence on the authentic substance, structure andaesthetics of the monument. Comparing such different fields of heritage protection is possible thanks toimplementation of numerical factors, which allows evaluation of the grade of intervention in historicalsubstance of historic objects and their neighborhood. Although numerical evaluation could neverfully replace interdisciplinary analysis, it might be helpful for the decision makers (e.g., officials inheritage office) in choosing the optimal technology in relatively straightforward cases.

The final evaluation (Ee) of each method assessed is determined by the formula:

Ee = mr ×ms ×mc ×ma (1)

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where:

mr—risk factor;ms—structural score;mc—conservation assessment;ma—architectural score.

Risk factor (mr) depends on geotechnical and hydrological conditions, quality of drilling machines,qualities and experience of the drill operators and reliability of the applied reinforcement technology.Its maximum value is 1.0. In order to save space, the risk evaluation has been skipped in this case(in the paper).

The structural score (ms) must be assigned to a failure mode. Generally, depending on the structuralelement, different mechanisms of destruction can take place. However, the most important is thecritical one. In the case considered, the wall deflection was assumed as the critical one. The structuralscore is calculated by the formula:

ms = (−0.1u + 1.5) (2)

where: ms—structural score, represents effectiveness of stabilization methods compared to displacement;u—displacement (cm).

The structural score (ms) was based on the Polish Standards [47], which rate the effectiveness of agiven method on a scale from 0 to 1; value ms = 1 corresponds to full safety. Normal wall deflectionshould be no larger than 0.6 cm/m, which means that umax = 5.0 cm for the entire height of the wall.It was assumed that this value corresponds to 100% safety (ms = 1). The current wall deflection(about 15 cm) corresponds to the emergency condition, i.e., 0% safety (ms = 0).

The conservation assessment (mc) is defined as the preservation degree of the authenticity ofmonuments by the following formula:

mc =(1−

VwdVw

)×

(1−

VsdVs

)(3)

where:

Vwd —volume of disturbed authentic historic wall;Vw —volume of authentic historic wall;Vsd—volume of disturbed authentic soil covering the wall;Vs—volume of authentic soil covering the wall in impact area.

The preservation degree of the authenticity of monuments is determined by the average of twovalues, in line with Formula (3). The first value (Vwd/Vw) is a ratio of volume Vwd of disturbed authentichistoric wall altered by the application of a given technology (e.g., borehole) to the total volume Vw ofauthentic historic wall. The second (Vsd/Vs) is the ratio of the volume of disturbed authentic soilcovering the wall Vsd by applied technology or archeological excavation to the volume of authenticsoil Vs. Because the reversibility of the materials is almost always contrary to the protection of thehistorical substance (instead of the shape), the authors decided that the spatial indicators illustratingthe transformation of the original monuments should be an adequate method of describing the scale ofchanges. Moreover, they might be easily adopted in the proposed formula.

The architectural (ma) score is based on the degree of the covered surface by the new designedstructural solution to the total wall surface described by the formula:

ma =(1−

AdAt

)(4)

where:

Ad—covered surface of the wall or/and its neighboring area;At—total surface area of the wall above the ground.

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The surface covered by the new designed structural solution is determined by the scale of theimpact on the area around the monument, in line with Formula (4). The value (Ad/At) is a ratio ofthe covered surface area Ad of the wall (or its neighboring area) altered by the application of a giventechnology (e.g., scaffolding) to the total surface area At of the wall above the ground.

The authors decided to scope their research to a single case study because they wanted to builda comparable evidence base of popular repairing techniques. That is the reason why the authorsavoided analyzing the repairs in different monuments, which always was based on individual studies.Although such a strategy would have been preferable in most heritage studies, it does not allow fortesting the S–C–A method. Therefore, the methodology described above was applied in the evaluationof the repair technique of the retaining wall in the Wisłoujscie Fortress.

3. Research Object

The Wisłoujscie Fortress (Figure 1) is an example of well-preserved fortification and hydrotechnicalengineering from the Middle Ages and early Modern Era. The President of the Republic of Polanddecided in 2018 to award this monument the highest level of protection by including it on the PolishHeritage List as a “Historic Monument” [48].

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At—total surface area of the wall above the ground.

The surface covered by the new designed structural solution is determined by the scale of the impact on the area around the monument, in line with Formula (4). The value (Ad/At) is a ratio of the covered surface area Ad of the wall (or its neighboring area) altered by the application of a given technology (e.g., scaffolding) to the total surface area At of the wall above the ground.

The authors decided to scope their research to a single case study because they wanted to build a comparable evidence base of popular repairing techniques. That is the reason why the authors avoided analyzing the repairs in different monuments, which always was based on individual studies. Although such a strategy would have been preferable in most heritage studies, it does not allow for testing the S–C–A method. Therefore, the methodology described above was applied in the evaluation of the repair technique of the retaining wall in the Wisłoujście Fortress.

3. Research Object

The Wisłoujście Fortress (Figure 1) is an example of well-preserved fortification and hydrotechnical engineering from the Middle Ages and early Modern Era. The President of the Republic of Poland decided in 2018 to award this monument the highest level of protection by including it on the Polish Heritage List as a “Historic Monument” [48].

Figure 1. The aerial photo of the Wisłoujście Fortress in Gdańsk, Poland (2019).

The retaining wall—the main subject of this paper—was primarily built as a part of another structure, the lieutenant’s quarter, used later as an auxiliary building [49]. The ground-floor building, erected on a rectangular plan, was situated by the northern curtain wall of the Fort Carré in the first half of 17th century.

Unlike the main barracks, which were located in the eastern wall of the fort and covered by ground, the building mentioned was covered by a steep roof reaching over the curtain wall. This was probably the reason why this construction was demolished in early 19th century, either during the Napoleonic Wars, when the fortress was besieged twice in 1807 and 1813, or shortly after. The northern part of the demolished building was turned into the retaining wall, although it had never been designed for that purpose (Figure 2). In the second half of the 19th century, when military authorities decided to strengthen the structure of the Fortress, an external layer of bricks was added to the wall. It also became necessary to build a buttress of the wall which was situated by the west side of the demolished building. The next alterations or works were not conducted in the area of the

Figure 1. The aerial photo of the Wisłoujscie Fortress in Gdansk, Poland (2019).

The retaining wall—the main subject of this paper—was primarily built as a part of anotherstructure, the lieutenant’s quarter, used later as an auxiliary building [49]. The ground-floor building,erected on a rectangular plan, was situated by the northern curtain wall of the Fort Carré in the firsthalf of 17th century.

Unlike the main barracks, which were located in the eastern wall of the fort and covered byground, the building mentioned was covered by a steep roof reaching over the curtain wall. This wasprobably the reason why this construction was demolished in early 19th century, either during theNapoleonic Wars, when the fortress was besieged twice in 1807 and 1813, or shortly after. The northernpart of the demolished building was turned into the retaining wall, although it had never been designedfor that purpose (Figure 2). In the second half of the 19th century, when military authorities decidedto strengthen the structure of the Fortress, an external layer of bricks was added to the wall. It alsobecame necessary to build a buttress of the wall which was situated by the west side of the demolishedbuilding. The next alterations or works were not conducted in the area of the retaining wall until

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the removal of neglected greenery in the 1990s. It is likely that the use of heavy machines made itnecessary for the deflected wall to be subsequently supported by two wooden buttresses.

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retaining wall until the removal of neglected greenery in the 1990s. It is likely that the use of heavy machines made it necessary for the deflected wall to be subsequently supported by two wooden buttresses.

Figure 2. Sections through the auxiliary building and the retaining wall in the Wisłoujście Fortress. The schemes of transformations.

The alterations to the wall described above contributed to its current state of deformation. It is evident that no basic stability requirements for such wall—neither overturning about its toe nor sliding along its base—are met (Figure 3C). However, after demolition of the auxiliary building at the beginning of the 19th century, the retaining wall did not collapse. The actual stability is a result of the combination of the following: (1) the spatial rigidity of the wall’s structure due to its irregular shape (Figure 1), (2) adding of the buttress which supported the wall and (3) the real active pressure decreased due to the wall deformation that had already occurred in the past.

Figure 3. The retaining wall after its repairs from the second half of the 19th century: (A). The interface

between the original wall and the 19th century siding layer, (B). Current geometry of the wall, (C). Scheme of water circulation in the wall

The impact of greenery might be considered as another hypothetical reason for the deflection of the wall. There were wild bushes growing on top of the curtain wall, which might have caused some structural failure [50,51]. Although the whole construction was kept in good condition until the 1930s, the greenery was not pruned after the Second World War. In any case, the excavations in 2016 did not confirm whether the roots could have harmed the retaining wall.

Because the wall did, in fact, resist earth pressure for about 130 years, numerous vertical cracks have appeared on the surface of the wall, approximately within 0.5–2.3 m from each other (Figure 4). There is also surface freeze–thaw cycle damage visible on the wall, which could, to an untrained eye, look like cracks. Since the second half of the 19th century, two significant series of repairs have been carried out. The first was the addition of a 25 cm-thick brick siding layer and the second one was a buttress. The new facing (Figures 3A,B and 5) was added without re-walling, which, paradoxically, led to deterioration of masonry over time: a crevice that developed between the new and old walls collected water (Figure 4). At low temperatures, the water froze, bursting the wall and causing bulges in its upper part (150 cm from the top of the wall), which increased its deviation from the vertical (see Figure 3). In 2016, the deviation from plumb amounted to approximately 15 cm.

Figure 2. Sections through the auxiliary building and the retaining wall in the Wisłoujscie Fortress.The schemes of transformations.

The alterations to the wall described above contributed to its current state of deformation.It is evident that no basic stability requirements for such wall—neither overturning about its toe norsliding along its base—are met (Figure 3C). However, after demolition of the auxiliary building at thebeginning of the 19th century, the retaining wall did not collapse. The actual stability is a result ofthe combination of the following: (1) the spatial rigidity of the wall’s structure due to its irregularshape (Figure 1), (2) adding of the buttress which supported the wall and (3) the real active pressuredecreased due to the wall deformation that had already occurred in the past.

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retaining wall until the removal of neglected greenery in the 1990s. It is likely that the use of heavy machines made it necessary for the deflected wall to be subsequently supported by two wooden buttresses.

Figure 2. Sections through the auxiliary building and the retaining wall in the Wisłoujście Fortress. The schemes of transformations.

The alterations to the wall described above contributed to its current state of deformation. It is evident that no basic stability requirements for such wall—neither overturning about its toe nor sliding along its base—are met (Figure 3C). However, after demolition of the auxiliary building at the beginning of the 19th century, the retaining wall did not collapse. The actual stability is a result of the combination of the following: (1) the spatial rigidity of the wall’s structure due to its irregular shape (Figure 1), (2) adding of the buttress which supported the wall and (3) the real active pressure decreased due to the wall deformation that had already occurred in the past.

Figure 3. The retaining wall after its repairs from the second half of the 19th century: (A). The interface

between the original wall and the 19th century siding layer, (B). Current geometry of the wall, (C). Scheme of water circulation in the wall

The impact of greenery might be considered as another hypothetical reason for the deflection of the wall. There were wild bushes growing on top of the curtain wall, which might have caused some structural failure [50,51]. Although the whole construction was kept in good condition until the 1930s, the greenery was not pruned after the Second World War. In any case, the excavations in 2016 did not confirm whether the roots could have harmed the retaining wall.

Because the wall did, in fact, resist earth pressure for about 130 years, numerous vertical cracks have appeared on the surface of the wall, approximately within 0.5–2.3 m from each other (Figure 4). There is also surface freeze–thaw cycle damage visible on the wall, which could, to an untrained eye, look like cracks. Since the second half of the 19th century, two significant series of repairs have been carried out. The first was the addition of a 25 cm-thick brick siding layer and the second one was a buttress. The new facing (Figures 3A,B and 5) was added without re-walling, which, paradoxically, led to deterioration of masonry over time: a crevice that developed between the new and old walls collected water (Figure 4). At low temperatures, the water froze, bursting the wall and causing bulges in its upper part (150 cm from the top of the wall), which increased its deviation from the vertical (see Figure 3). In 2016, the deviation from plumb amounted to approximately 15 cm.

Figure 3. The retaining wall after its repairs from the second half of the 19th century: (A). The interfacebetween the original wall and the 19th century siding layer, (B). Current geometry of the wall,(C). Scheme of water circulation in the wall.

The impact of greenery might be considered as another hypothetical reason for the deflection ofthe wall. There were wild bushes growing on top of the curtain wall, which might have caused somestructural failure [50,51]. Although the whole construction was kept in good condition until the 1930s,the greenery was not pruned after the Second World War. In any case, the excavations in 2016 did notconfirm whether the roots could have harmed the retaining wall.

Because the wall did, in fact, resist earth pressure for about 130 years, numerous vertical crackshave appeared on the surface of the wall, approximately within 0.5–2.3 m from each other (Figure 4).There is also surface freeze–thaw cycle damage visible on the wall, which could, to an untrainedeye, look like cracks. Since the second half of the 19th century, two significant series of repairs havebeen carried out. The first was the addition of a 25 cm-thick brick siding layer and the second onewas a buttress. The new facing (Figure 3A,B and Figure 5) was added without re-walling, which,paradoxically, led to deterioration of masonry over time: a crevice that developed between the newand old walls collected water (Figure 4). At low temperatures, the water froze, bursting the wall and

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causing bulges in its upper part (150 cm from the top of the wall), which increased its deviation fromthe vertical (see Figure 3). In 2016, the deviation from plumb amounted to approximately 15 cm.

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Figure 4. The retaining wall in the Wisłoujście Fortress: (A). Overall view; (B). Analyzed part of the retaining

wall (photo taken in 2016); (C). Schematic pattern of cracks and damages

In conclusion, the primary reason for structural failure of the wall is associated with its structural characteristics (Figure 4). However, some cracks observed nowadays may have developed accidentally, due to pressure increase during the removal of greenery. Finally, the retaining wall had lost its stability in the past and had to be strengthened by the temporary wooden buttress (Figure 4A). Therefore, it is impossible to confirm whether the inclination has stopped or it is still increasing.

4. Stabilization Methods

Five different methods of stabilization have been considered and are briefly discussed below.

4.1. Natural State

No intervention (Figure 5a); the condition and appearance of the wall will not change. A measured and calculated deflection of 15.0 cm means that there is a high probability of a construction disaster.

Figure 4. The retaining wall in the Wisłoujscie Fortress: (A). Overall view; (B). Analyzed part of theretaining wall (photo taken in 2016); (C). Schematic pattern of cracks and damages.

In conclusion, the primary reason for structural failure of the wall is associated with its structuralcharacteristics (Figure 4). However, some cracks observed nowadays may have developed accidentally,due to pressure increase during the removal of greenery. Finally, the retaining wall had lost its stabilityin the past and had to be strengthened by the temporary wooden buttress (Figure 4A). Therefore,it is impossible to confirm whether the inclination has stopped or it is still increasing.

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Figure 5. The repairing methods of the retaining wall. (a) Natural state; (b) relieving shelf; (c) passive anchors (nails); (d) CFA 3 CFA (continuous flight augering) piles;(e) jet grouting; (f) buttress.

4.2. Relieving Shelf

The relieving shelf is a slab 1.8 m long and 0.3 m thick, inserted 2.0 m below the ground surface. The shelf is anchored to the wall (Figure 5b) and reduces soil pressure. The reinforcement is laid in a previously prepared excavation, nested in the wall and then poured over with concrete. Finally, the excavation is filled up with soil. Making a groove in the wall destroys the structure of the wall on the invisible side and requires digging a ditch in the rampart. Furthermore, archaeological excavations should be carried out before making the shelf. After the works have been completed, the alterations will be invisible. The technology is simple, easy to apply and inexpensive. The only technical difficulty is connecting the relieving shelf to the wall.

4.3. Passive Anchors (Nails)

Installation of passive anchors requires drilling through the wall (Figure 5c). Each borehole is then filled with a cement paste. The anchor itself, in the form of a steel bar with a diameter of 6 cm

Figure 5. The repairing methods of the retaining wall. (a) Natural state; (b) relieving shelf; (c) passiveanchors (nails); (d) CFA 3 CFA (continuous flight augering) piles;(e) jet grouting; (f) buttress.

4. Stabilization Methods

Five different methods of stabilization have been considered and are briefly discussed below.

4.1. Natural State

No intervention (Figure 5a); the condition and appearance of the wall will not change. A measuredand calculated deflection of 15.0 cm means that there is a high probability of a construction disaster.

4.2. Relieving Shelf

The relieving shelf is a slab 1.8 m long and 0.3 m thick, inserted 2.0 m below the groundsurface. The shelf is anchored to the wall (Figure 5b) and reduces soil pressure. The reinforcementis laid in a previously prepared excavation, nested in the wall and then poured over with concrete.Finally, the excavation is filled up with soil. Making a groove in the wall destroys the structure of the

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wall on the invisible side and requires digging a ditch in the rampart. Furthermore, archaeologicalexcavations should be carried out before making the shelf. After the works have been completed,the alterations will be invisible. The technology is simple, easy to apply and inexpensive. The onlytechnical difficulty is connecting the relieving shelf to the wall.

4.3. Passive Anchors (Nails)

Installation of passive anchors requires drilling through the wall (Figure 5c). Each borehole isthen filled with a cement paste. The anchor itself, in the form of a steel bar with a diameter of 6 cm anda length of 3.6 m, is cemented inside the hole. The hole has a diameter of 10 cm. The spacing betweenthe anchors is 3.0 m. Drilling disturbs the original structure of the wall, leaves the head in its outer faceand changes the structure of unexamined (not yet excavated) soil, which might have archeologicalvalue. The effect of anchoring on the appearance of the wall will be minimized by masking the anchorsunder a siding layer or by using eight masking plates. Adding an inappropriate, disproportionate oraesthetically unpleasant feature may affect the visual assessment. Due to the control of the anchorinstallation, this method is very safe and effective.

4.4. CFA Piles

This method involves making a palisade of reinforced concrete piles approximately 1.5 m behindthe wall (Figure 5d). The palisade decreases the soil pressure on the structure. Piles with a diameter of0.40 m and a length of 7.0 m are spaced every 0.50 m. The piles themselves do not alter the structureof the wall but the insertion procedure disturbs the soil by drilling, stirring and pulling it to thesurface when the drill bit is removed. Furthermore, if the drill bit encounters an object larger than itsdiameter, the object will be drilled through or pushed aside. This technology can cause an additionalbulging of the wall resulting from the operation of the drill and the weight of the drilling machine.For these reasons, a temporary support of the wall should be put in place for the duration of the drilling.The piles will not be visible. There is a risk of damaging the wall during the installation of the piles.

4.5. Jet Grouting

This method is about reinforcing soil under the existing foundation of the wall by injection ofcement paste at a very high pressure. The dimensions of the reinforced foundation are 0.80 × 2.30 m(Figure 5e). This technology does not damage the original surface of the wall as it affects only thesoil under the wall foundation. In order to conduct archaeological excavations safely, it wouldbe necessary to dig up the soil along successive sections of the wall, on its both sides. This is,however, hardly practicable as it involves extensive intervention in the ramparts, which remain underarchaeological protection. The entire procedure is, therefore, costly. For these reasons, it was assumedthat the excavations would be carried out in front of and under the wall (see Figure 5e). The changeswill be invisible.

4.6. Buttress

The buttress supporting the wall has the following dimensions: 0.65 m × 0.45 m × 3.0 m(thickness ×width × height); the buttress reaches 1.1 m deep into the ground. It is the oldest reinforcementmethod applied to retaining walls and it involves making a brick buttress, which counteracts both soilpressure and tilting of the wall (Figure 5f). Seven buttresses (one already exists) supporting the wallwill affect its original structure over the surface area. The soil down to the buttress foundation needsto be examined so that excavations can be performed before bricklaying. The excavation for each ofthe buttresses will have a depth of 1.0 m and a surface area of 1.5 × 1.5 m. The new foundations willhave dimensions of 0.5 × 0.65 × 0.45 m. Technology makes it possible to determine the dimensions ofbuttresses that would be sufficient to prevent the wall from further tilting.

Sustainability 2020, 12, 8570 10 of 16

5. Numerical Analysis

The purpose of the numerical analysis was to determine the effectiveness of the selected methodsin strengthening and stabilizing the wall. The analysis was performed by the two-dimensional explicitFinite Difference Method (FD), using the FLAC2D software [45]. This method is an accurate andversatile approach to the analysis of both stability and displacement of retaining walls. It allowsfor calculating the field of displacement both in the soil mass and in the engineering structures,which are considered as appropriate for the stabilization and strengthening of the wall. Its stabilitywas assessed based on the safety factor F, which is calculated using strength reduction techniquefundamentals. The additional advantage of the proposed method is that it makes no assumptions aboutthe failure mechanism—especially for simple geometry. In contrast to the traditional “limit equilibrium”analysis, this method provides a full solution to the coupled stress/displacement, equilibrium andconstitutive equations. The calculations were based on the so-called “strength reduction technique” [52].Geotechnical studies [53] have shown that the groundwater level is currently 2.0 meters below the baseof the wall foundation. The substratum is composed mainly of fine and medium sand (Figure 6A),and the earthwork that loads the retaining wall consists of fine sand and brick debris. The soil densityindex in the rampart body (ID) is 0.2. Table 1 presents the parameters of soil layers in the calculationmodel. The diversity of soils in the Ia-Id layers results from their different degrees of compaction,ranging from 0.30 for the layer Ia to 0.70 for the layer Id. On the basis of laboratory tests, the averagecompressive strength of old bricks was determined to be equal to 15.8 MPa, mortar equal to 0.75 MPaand new ones (from external wall)—equal to 34.1 MPa and 19.3 MPa [52].Sustainability 2020, 12, x FOR PEER REVIEW 11 of 16

.

Figure 6. The numerical model of the retaining wall: (A) division of the model into geotechnical layers; (B) displacement vectors

The values of wall crown displacements were obtained by numerical calculations in all the cases, which made it possible to identify the methods meeting the criterion umax = 5 cm. Table 2 provides the maximum calculated displacement values for the stabilization methods assessed in the analysis.

Table 2. Maximum displacement for the wall stabilization methods analyzed.

Lp. State umax (cm)

0 Natural state 15.21

1 Relieving shelf 3.16

2 Passive anchors 1.27

3 CFA piles 5.28

4 Jet grouting 2.42

5 Buttresses 0.76

On the basis of the results summarized in Table 2, the considered stabilization options can be ranked. The diagrams (models) of particular stabilization methods are also presented, including the current (natural) state of the wall.

It should be noted that no experimental verification of the calculation results regarding the influence of each stabilization method is currently possible; no stabilization works were completed so far. Nevertheless, given the carefully determined parameters of the soil and the wall materials in combination with the characteristics of the advanced numerical tool that is the FLAC2D algorithm, the calculation results in all variants are reliable and represent both physical qualities and behavior of the object accurately. The fields of stress and displacement express, precisely, the influence of all stabilization measures and methods. As it can be seen in Table 2, buttress support turned out to be the most effective stabilization countermeasure. In all stabilization cases, the maximum displacement is significantly lower (in the case of buttresses, by even more than 20 times) in comparison with the displacement of the original wall. It proves the high potential effectiveness of any stabilization method.

The relationship between the calculated displacement of the wall’s crown and the structural score calculated by (Formula (2)) is presented graphically in Figure 7.

Figure 6. The numerical model of the retaining wall: (A) division of the model into geotechnical layers;(B) displacement vectors.

First, the current original state of the wall was examined by the “back analysis” method,i.e., the variant without wall stabilizing measures. The aim was to determine the values of strengthparameters (cohesion and angle of internal friction of the soil constituting the earthwork that putspressure against the wall), for which the measured and calculated displacements of the wall crownwould be the same. It means that, by contrast to other parameters determined in the tests, these twostrength parameters (i.e., cohesion and angle of friction) are found at the base of calculations using a“trial and error” approach and FLAC2D code. A numerical model and displacement vectors are shownin Figure 6. Calculated maximum displacement (u) of the wall’s crown was equal to 15.21 cm.

The values of wall crown displacements were obtained by numerical calculations in all the cases,which made it possible to identify the methods meeting the criterion umax = 5 cm. Table 2 provides themaximum calculated displacement values for the stabilization methods assessed in the analysis.

Sustainability 2020, 12, 8570 11 of 16

Table 1. The parameters of soils and construction materials derived from ref. [PN-81/B-03020].

Soil, Material Unit Weight(kN/m3)

Shear ElasticityModulus G (MPa)

Bulk ElasticityModulus K (MPa)

Cohesionc (kPa)

Angle ofFriction (◦)

Brick wall 18.0 192.3 416.7 0 33Embankment 18.0 98.0 21.25 0 25

Soil in the earthwork ID = 0.20 18.0 19.23 41.67 0.31 26Layer Ia (fine and medium sand),

ID = 0.30 (*) 18.0 15.38 33.33 0 29

Layer Ib (fine and medium sand),ID = 0.40 18.5 23.85 44.17 0 30

Layer Ic (fine and medium sand),ID = 0.50 19.0 20.38 51.67 0 30.5

Layer Id (fine and medium sand),ID = 0.60 19.5 28.85 62.5 0 31

Layer Ie (fine and medium sand),ID = 0.70 20.0 32.7 70.8 0 31.5

Buttress (brick) 18.0 102.2 222.2 667 21.8

(*) ID means soil density index.

Table 2. Maximum displacement for the wall stabilization methods analyzed.

Lp. State umax (cm)

0 Natural state 15.211 Relieving shelf 3.162 Passive anchors 1.273 CFA piles 5.284 Jet grouting 2.425 Buttresses 0.76

On the basis of the results summarized in Table 2, the considered stabilization options can beranked. The diagrams (models) of particular stabilization methods are also presented, including thecurrent (natural) state of the wall.

It should be noted that no experimental verification of the calculation results regarding theinfluence of each stabilization method is currently possible; no stabilization works were completedso far. Nevertheless, given the carefully determined parameters of the soil and the wall materials incombination with the characteristics of the advanced numerical tool that is the FLAC2D algorithm,the calculation results in all variants are reliable and represent both physical qualities and behaviorof the object accurately. The fields of stress and displacement express, precisely, the influence of allstabilization measures and methods. As it can be seen in Table 2, buttress support turned out to bethe most effective stabilization countermeasure. In all stabilization cases, the maximum displacementis significantly lower (in the case of buttresses, by even more than 20 times) in comparison with thedisplacement of the original wall. It proves the high potential effectiveness of any stabilization method.

The relationship between the calculated displacement of the wall’s crown and the structural scorecalculated by (Formula (2)) is presented graphically in Figure 7.

It is seen in Figure 7 that the calculated displacement of the wall’s crown in the case of the relievingshelf is 3.16 cm and corresponds to 18.4% above the required level of safety, whereas the displacementof the wall’s crown for buttress is 0.76 cm and corresponds to 42.2% above the required level of securityand so on.

Sustainability 2020, 12, 8570 12 of 16Sustainability 2020, 12, x FOR PEER REVIEW 12 of 16

.

Figure 7. The displacement of the wall crown.

It is seen in Figure 7 that the calculated displacement of the wall's crown in the case of the relieving shelf is 3.16 cm and corresponds to 18.4% above the required level of safety, whereas the displacement of the wall’s crown for buttress is 0.76 cm and corresponds to 42.2% above the required level of security and so on.

6. Evaluation of the S–C–A Method

The partial and final results of the S–C–A methodology are summarized in Table 3. There are also relevant volume or area values included here, appearing in Formulas (3) and (4), as well as particular, individual assessments. The presented data allow comparing the results which were achieved for three different fields of heritage protection: structural, conservational and aesthetical.

Table 3. Comparison of the impact of conservational, architectural and structural conditions on the assessment of the wall stabilization technology.

u Vwd Vw Vsd Vs Ad At mc ma mr ms Ee (cm) (m3) (m3) (m3) (m3) (m2) (m2) (-) (-) (-) (-) (-)

1. Natural state 15.00 0.00 95.53 0.00 311.25 0.00 84.5 1.000 1.000 1.0 0.000 0.000 2. Relieving shelf 3.16 1.91 95.53 123.71 311.25 0.00 84.5 0.590 1.000 1.0 1.184 0.699 3. Passive anchors 1.27 0.06 95.53 82.80 311.25 0.09 84.5 0.733 0.999 1.0 1.373 1.006

4. CFA piles 5.28 0.00 95.53 21.99 311.25 0.00 84.5 0.929 1.000 1.0 0.972 0.903 5. Jet grouting 2.42 0.00 95.53 95.98 311.25 0.00 84.5 0.692 1.000 1.0 1.258 0.870

6. Buttress 0.76 0.00 95.53 13.50 311.25 14.6 84.5 0.957 0.828 1.0 1.424 1.128

According to the structural aspect (ms), it is proved that the best methods of repairing historical wall are buttress, passive anchors and jet grouting. However, some of them may cause too much integration in the authenticity of the monument, which degrades its heritage value. In spite of the constructional advantages, jet grouting and relieving shelf are the least acceptable methods of stabilization because of the scale of integration in the historical substance of the wall (see Table 3). It impacts the final evaluation (Ee). It is worth noting that buttresses achieved relatively the worst score in the ranking of aesthetic values (ma) but were the mostly accepted method of strengthening the historic construction in previous eras. What is more, a similar structure was erected for the analyzed wall in the 19th century and its impact on the authenticity of the monument was very limited. On the other hand, minimizing the space between new buttresses may cause deterioration of the aesthetical factor.

Figure 7. The displacement of the wall crown.

6. Evaluation of the S–C–A Method

The partial and final results of the S–C–A methodology are summarized in Table 3. There are alsorelevant volume or area values included here, appearing in Formulas (3) and (4), as well as particular,individual assessments. The presented data allow comparing the results which were achieved for threedifferent fields of heritage protection: structural, conservational and aesthetical.

Table 3. Comparison of the impact of conservational, architectural and structural conditions on theassessment of the wall stabilization technology.

u Vwd Vw Vsd Vs Ad At mc ma mr ms Ee(cm) (m3) (m3) (m3) (m3) (m2) (m2) (-) (-) (-) (-) (-)

1. Natural state 15.00 0.00 95.53 0.00 311.25 0.00 84.5 1.000 1.000 1.0 0.000 0.0002. Relieving shelf 3.16 1.91 95.53 123.71 311.25 0.00 84.5 0.590 1.000 1.0 1.184 0.6993. Passive anchors 1.27 0.06 95.53 82.80 311.25 0.09 84.5 0.733 0.999 1.0 1.373 1.006

4. CFA piles 5.28 0.00 95.53 21.99 311.25 0.00 84.5 0.929 1.000 1.0 0.972 0.9035. Jet grouting 2.42 0.00 95.53 95.98 311.25 0.00 84.5 0.692 1.000 1.0 1.258 0.870

6. Buttress 0.76 0.00 95.53 13.50 311.25 14.6 84.5 0.957 0.828 1.0 1.424 1.128

According to the structural aspect (ms), it is proved that the best methods of repairing historicalwall are buttress, passive anchors and jet grouting. However, some of them may cause too muchintegration in the authenticity of the monument, which degrades its heritage value. In spite ofthe constructional advantages, jet grouting and relieving shelf are the least acceptable methods ofstabilization because of the scale of integration in the historical substance of the wall (see Table 3).It impacts the final evaluation (Ee). It is worth noting that buttresses achieved relatively the worstscore in the ranking of aesthetic values (ma) but were the mostly accepted method of strengtheningthe historic construction in previous eras. What is more, a similar structure was erected for theanalyzed wall in the 19th century and its impact on the authenticity of the monument was very limited.On the other hand, minimizing the space between new buttresses may cause deterioration of theaesthetical factor.

The S–C–A method allows for understanding how different modes of repairing the historicconstruction may influence its protection. Consequently, there is no one proper method of strengtheningthe wall because each of them devastate some part of it. Comparison of each partial score shows thatthe optimal method is strengthening the wall with buttresses, but passive anchors are acceptable as well.

Sustainability 2020, 12, 8570 13 of 16

The highest ranking achieved by this method resulted, for the most part, from its high structural (ms)and conservation (mc) score, due to the most favorable ratio of the volume of disturbed soil (Vsd) to thevolume of the authentic soil (Vw) covering the wall. The second and fourth column of Table 3 representthe values of the altered surface area of the wall and the volume of soil to be excavated for each of theassessed methods. The conservational, structural and, particularly, architectural assessments presentedin the eighth, ninth and eleventh column of the table are objective. Subsequent columns show theresults of calculations assuming different values of impact factors representing the relative importanceascribed to the conservational, structural and architectural aspects.

It seems that the highest value of the risk factor mr corresponds to the relieving shelf and thelowest mr corresponds to jet grouting. However, this factor should be evaluated on the basis of moreprecise research, which is not the subject of this paper. In the following calculations, the risk factormr = 1.0 is assumed.

Some disadvantages of certain technologies should be mentioned as well. In the case of CFA piles,a problem may arise from the limited access of the drilling machine, whose weight, depending on themodel, ranges between 8 and 20 t. It is therefore necessary to check and secure the route of the machineto the working zone and to evaluate the wall conditions during its operation. Additional pressure onthe soil resulting from drilling is another difficulty associated with the use of CFA piles. A disadvantageof jet grouting is the risk of collapse of the grouted zone, caused by a low strength of the mixtureof organic soil and cement mass. It is vital to use appropriate pressure and density of the injectedmixture; incorrect selection of these quantities may result in the formation of voids. Furthermore,a large amount of liquid spoil created during jet grouting has a negative impact on the quality andaesthetics of the construction site. Finally, the relatively large spacing (3 m) of buttresses can be anissue: the zones between them lack any stabilizing element, so the wall sections between the buttressesmay still become unstable.

7. Conclusions

The authenticity of historical buildings is thought to be so precious because when once destroyed,they will never be reconstructed. Thus, material heritage could be treated as a non-renewable resource.Finding the right balance between keeping monuments intact and present necessities is, however,an open question. Seeking the proportions between factors determined by different fields of sciencemakes the S–C–A method resemble the theory of sustainable development. Legal framework requiresan administrative act—a decision by conservation officers who must take into account conservational,architectural and structural factors. Sometimes, the authorities seek help from experts, but in theend, the decision is theirs, and as a consequence, the outcomes vary due to differences in the officers’knowledge and experience. Therefore, the proposed method might be applied to improve therelations between stakeholders involved in repairing the historical structures (engineers, architects andconservation officers). It would help not only in the communication process but also in preselectingthe best solutions. Although the authors are aware of the significance of personal expertise, there isa need for a more verifiable approach, an evidence-based method for evaluation of interventions inhistorical structures.

That is the reason why this paper’s focus is on the retaining wall instead of the entire FortCarré or group of different monuments. As the authors proved, the wall is representative of thepractical problems that typically arise with monument conservation. Even though the differentmethods of stabilizing walls could be ranked (Table 3), selection of the most appropriate one might bechallenging. This is mainly because the final conservation assessment and, above all, the architectural(aesthetic) assessment are, to some degree, subjective, even if quantified (mc; ma). In contrastto the strictly objective structural assessment—based on the displacement criterion—they rely onnon-measurable criteria, such as the quality of expertise and experience of the actors involved.In addition, certain solutions may encounter resistance from a conservation officer, who may havelimited knowledge of engineering technologies. Nevertheless, the approach proposed in this paper may

Sustainability 2020, 12, 8570 14 of 16

serve—at least in some cases—as an auxiliary tool in decision-making. Optimization of stabilizationsystems in the protection of cultural heritage must meet additional requirements, such as conservationand/or aesthetic (architectural) ones. Before they are used in the optimization procedure, they shouldbe subjected to a quantitative, possibly objective, assessment. The issues pertaining to the costs ofrenovation of historical buildings are of secondary importance. In these cases, classic, i.e., structural oreconomic, optimization needs to be significantly modified.

The proposed S–C–A method has been checked in the case of the retaining wall and, undoubtedly,needs more complex tests in further research. This paper, however, aimed to present a newproposition about the multi-criteria technique of selecting the solution of repairing basic monuments.Although professional interdisciplinary research into historical buildings must be undertaken in allinstances of emergency engineering interventions before designing an actual solution could evencommence, the presented algorithm might be useful for engineers in choosing the best variant of repair,and it helps in communication between different stakeholders.

Author Contributions: Conceptualization, P.C., J.P. and P.S.; methodology, J.P., P.S. and L.Z.; investigation,P.C. and L.Z.; resources, P.C.; data curation, P.C.; writing—original draft preparation, P.C., J.P., P.S. and L.Z.;writing—review and editing, P.C., J.P. and P.S.; visualization, P.C.; supervision, J.P., P.S. and L.Z. All authors haveread and agreed to the published version of the manuscript.

Funding: This research received no external funding.

Conflicts of Interest: The authors declare no conflict of interest.

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